A characterization of associativity

Abstract

A necessary and sufficient condition for associativity of a function is given, in terms of a particular relation being a function. The concept of an associative function is generalized to the concept of a function being asssociative relative to a sequence and a characterization of such relative associativity is also given. These two characteristics are applied to the problem of proving the associativity, or relative associativity, of a function.